Hello Bill, your observation is well-known. It is simply because of the fact that by N=p1*p2*p3*... +px the p1, p2, p3… are excluded as prime divisors and...
Let px, px+1 be consecutive primes, N=product of optional primes up to px or =1, M=product of the lacking primes up to px or =1, then abs(N+-M) is prime, if...
Conjecture: Every prime number Q can be written as Q = absolute(N+-M), where N,M = natural numbers, coprime and products of powers of primes pi^ai (i = ...
In order to make it clearer: I state, if one distributes all possible powers of all prime numbers in the indicated way on the products N and M and makes...
Hello, Group. Let n= 1, 2, 3, etc. and Nn= 3^n -2. Does the sequence 1, 7, 25, 79, 241, 727, 1185, etc. have a test for verifying the primality of Nn similar...
... No. Note N+1 == 3^n-2+1 == 3^n-1 and N-1 == 3^n-2-1 == 3*(3^(n-1)-1 So given enough factors of N+-1 the combined "classical tests" can be used: ...
Here's a curio I just submitted to the Prime Pages: We look for a pair of numbers (m,n) each less than p=29 such that six simultaneous primes are generated: ...
Hi, John Renze's PARI chg.gp script has just finished a test of 4955-digit number 4^8230-3 = 2^16460-2-1 (as some people prefer). It is the largest prime...
Hello, This email message is a notification to let you know that a file has been uploaded to the Files area of the primenumbers group. File :...
primenumbers@yahoogro...
Mar 3, 2006 4:53 am
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Hi I have added a new file under visualisation. The title is "The prime spiral, Goldbach & Eratosthenes". ( 34 pages, 750 kb). The first subject is my...
It is well known that for the expression (n+1)^x - n^x to yield a prime number, x must itself be prime. (And if x is a prime p the same expression contains...
I will be out of the office starting 03/04/2006 and will not return until 03/12/2006. I will respond to your message when I return. [Non-text portions of this...
... The following pfgw abc2 file ABC2 ($a+1)^$b-$a^$b // -f{$b} {number_primes,$b,1} a: from 1 to 10000 b: primes from 500 to 10000 with command pfgw –f...
... And according to Henri Lifchitz, the biggest ever found was (341233,3) which contains 205443 digits and was found by Jean Louis Charton last January. See...
... [snip] ... If I know, both, an ouput of pfgw (without -tc option) and Henri's pages, contain (strong, but) PRP's not primes. Mark has written about primes....
My mistake, I should have said probable prime instead of prime. (I used GP Pari without the -tc option.) Mark ... Henri's pages, ... primes. ... Selfridge] ......
Let seq(p) = 23571113171923...p seq(2) = 2 = prime seq(3) = 23 = prime seq(7) = 2357 = prime Is there any p > 7 for which seq(p) is prime? I tried up to p =...
... Well, I have a small archive of posts to the group before the group was moved to yahoo, and this was brought up before, here was the highest that anyone on...
... http://mathworld.wolfram.com/ConsecutiveNumberSequences.html says Eric Weisstein found no other prp's in the first 14897 terms. prime(14897) = 162623 gives...
A beautifull day, I have examine the prime numbers which lay on the polynom f(x)=x^2+x+1 My hypothese was : if 2^[(p-1)/3] = x or 2^[(p-1)/3] =x^2, then p is...
Restated, Bernhard is proposing the following: Let y = x^2 + x + 1 if x == 2^[(y-1)/3] mod y or if x^2 == 2^[(y-1)/3] mod y then y is a prime or else x+1 is a...
Hello All I have been spinning my wheels on a problem that I can not find an easy answer. So I thought I would ask before spinning my wheels trying to find a...
... The standard answer that you'll hear all of the time is that an optimized sieve can generate small primes faster than you can read them from a disk drive. ...
Apparently Bernhard is having trouble posting to the group, so I will mention that a prime guru found a counterexample to Bernhard's proposal, namely ****** ...
A beautifull day, ... I just calculate it for p=5 and p=7 and p=11, i have listed the numbers which are not primes, x, p, ifactor (x), ifactor (x+1): For p=5...
Thank you Bernhard for that data, way beyond what I could generate. So your generalized conjecture seems to be holding up thus far. I don't have the foggiest...
Hi all, Six primes are symmetrically arranged around the number 12: 5, 7, 11, (12) 13, 17, 19. Six primes are also symmtrically arranged around the number 15: ...
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